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What client are you using? Geth tends to have these problems with synchronizing with the network, especially when you use a GUI. You can use an online or local version of MEW. On the top right corner of MEW you can select the drop down menu and choose the Rinkeby testnet, and it will allow you to access your funds.

Be careful that you are using ONLY your testnet keystore/private key, as you do not want to expose your real Ether. Also make sure that if you use an online version, look for the green lock. If you're using a local version, verify the signatures if you have them.